(CNN) -- Fans of new media say Twitter, Facebook, MySpace and other social networking sites are changing the world.

They point to Barack Obama's 2008 presidential campaign, the 2009 demonstrations in Iran and Moldova's "Twitter Revolution" in Eastern Europe in 2009 as evidence that all those tweets and status updates are making a difference.

People want power online, and they can have it, but only in a particular way. Actress Alyssa Milano can help explain why.

Milano loves to tweet, and tweeters love Milano. She has 1 million followers who at any moment can learn how she eats, when she sleeps and what she reads. On September 15, unbeknownst to us, she tweeted about our book, "Connected," and included a direct link to its Amazon.com page.

You might expect our sales to skyrocket. They did not. If anything, our sales rank was lower in the 24-hour period after her tweet than before. We didn't sell a single extra copy.

This is not surprising. Online networks may be good for transmitting information, but they are usually not conduits for behavior change.

Although our research shows that obesity, happiness and even divorce can spread in networks between close friends, there is little evidence that behaviors spread between the tenuous relationships people have online.

On September 30, we mentioned this Twitter experience at a conference held in Washington by the American Legacy Foundation on the use of online networks to foster smoking cessation. It's very tough to quit smoking. But online networks connect motivated smokers to each other, and they seem to work.

Although the audience laughed when we showed them a slide with Milano looking grimly at our sales figures, one of the attendees thought that something was not right.

Susannah Fox of the Pew Research Center's Internet and American Life Project argued that if someone else, someone really influential, someone such as media mogul Tim O'Reilly, had sent the tweet, there might have been a different outcome.

So we contacted O'Reilly, and he graciously agreed to a little experiment.

On October 1, he too sent out a positive tweet about "Connected" that included a link to Amazon.com to his 1.5 million followers. This time, our sales rank did bounce a bit, but we estimate that we sold just one or two extra books. Given the number of followers he has, that's just a little better than the odds of getting struck by lightning. The mogul beat the actress, but not by much.

So who can we turn to for help if we want to use online social networks to influence people's behavior, whether for book sales or smoking cessation?

In our case, it was Fox who came to the rescue. A few days after O'Reilly, she sent her own tweet about "Connected." And although Fox has only 4,345 followers, we estimate that we sold three extra books as a result. A much smaller group of attentive followers, it turns out, may be more influenceable -- individually and collectively -- than the millions who follow the most famous tweeters.

These anecdotes comport with the more formal mathematical study of online interactions that we and others have been conducting over the past few years. And they suggest a number of important considerations regarding online influence.

First, it is not just the number of ties that matters online, it is also the nature and quality of these ties.

Malcolm Gladwell, author and staff writer for The New Yorker magazine, recently argued there was no hope that online social networks could be used for large-scale change. The reason is that the connections between people online are usually weak ties, not strong ties such as those to our family, next-door neighbors and real friends.

But this perspective overlooks something important. People do not just have countless weak ties online. Buried among all those weak ties are some strong ties. And they can make all the difference.

Online smoking cessation efforts work because people come to know and support each other to achieve something of mutual interest. And, under the right circumstances, the same thing can happen with political movements.

In 2008, for example, a 33-year-old Colombian engineer was able to mobilize 4.8 million people to attend rallies around the world to protest the holding of hostages by revolutionary groups in his country. But he started it with a group composed of himself and five close friends. And they in turn influenced other people with whom they had personal connections and with whom they shared a common goal, and so on.

Second, it is not just "influentials" who matter, but also "influenceables." O'Reilly and Milano can both be persuasive, and they are connected to millions of people. But it was the thousands of followers of Fox who ultimately won --granted, not by much -- our little contest. To make change happen, we need sheep as well as shepherds.

Finally, what is most important for efforts to harness the power of the internet to change people's behavior is this: We must learn how to cultivate online interactions that are, or feel, real.

We need interactions where something is actually at stake, such as the health status of the connected individuals, the business they are transacting, the game they are playing, the personal relationship they are maintaining or the political revolution they are fostering. When the circumstances are right, a shout can start an avalanche.

The opinions expressed in this commentary are solely those of the writers.